Solve the equation

Question

Solve the equation

8x+3y-5z=16

what is x?

what is y?

what is z?

 

Answer 1

there are infinite solutions.

 

you can plug in any numbers to x, y, and z to equal 16.

 

e.g.

 

let x = 8, y = 2, so

 

8(8) + 3(2) - 5z = 16

 

64 + 6 - 5z = 16

 

70 - 5z = 16

 

70 - 16 = 5z

 

5z = 54

 

z = 54/5

 

so what I'm saying is you can plug in any value to x or y and you will get a unique value for z

so there are infinite solutions.

Answer 2

By inspection and trial and error, one solution is x=1, y=1, and z=-1.

With only one equation with three unknowns, there is no algebraic solution. Normally three unknowns requires three separate equations of those unknowns!